The relation between level crossings, entanglement, and Berry phases is investigated for the Breit-Rabi Hamiltonian of hydrogen and sodium atoms, describing a hyperfine interaction of electron and nuclear spins in a magnetic field. It is shown that the entanglement between nuclear and electron spins is maximum at avoided crossings. An entangled state encircling avoided crossings acquires a marg...

The whole may be understood by its reconstruction from building block components: this is a LEG0 principle. A curve crossing diagram is a model for the reconstruction of energy profiles from Valence Bond (VB) building blocks, and may be considered as the quantum chemical analog of Robinson's curved arrow mnemonic. There are two archetypal diagrams which describe chemical transformations: (a) a ...

Nonradial oscillations of relativistic neutron stars with a solid crust are computed in the relativistic Cowling approximation, in which all metric perturbations are ignored. For the modal analysis, we employ three-component relativistic neutron star models with a solid crust, a fluid core, and a fluid ocean. As a measure for the relativistic effects on the oscillation modes, we calculate the r...

We present a model for ${\ensuremath{\chi}}^{(2)}$ waveguides accounting three modes, two of which make an avoided crossing at the second harmonic wavelength. introduce linearly coupled pure modes and adjust coupling to replicate waveguide dispersion near crossing. Analysis nonlinear system reveals continuous wave (CW) solutions across much parameter space prevalence its modulational instabilit...

We explain the concept of superadiabatic representations and show how in the context of electronically non-adiabatic transitions they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic potential energy surfaces near...

We study the relation between wavefunction (de)localization and avoided crossing in a quadrupole billiard. employ inverse participation ratio, Renyi entropy root-mean-square (rms) image contrast as three types of measures for (de)localization. It is found that all these behave similarly, exhibiting minimum at center crossing, where maximally delocalized. Our results show quantities can be good ...

We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, a...